US7508891B2ExpiredUtilityA1

Method for feeding back antenna shuffling information in a multiple-input multiple-output system using a multiple space-time block coding technique

80
Assignee: SAMSUNG ELECTRONICS CO LTDPriority: Jul 20, 2004Filed: Jul 14, 2005Granted: Mar 24, 2009
Est. expiryJul 20, 2024(expired)· nominal 20-yr term from priority
H04B 7/0639H04B 7/0417H04B 7/0697H04L 1/0687H04B 7/0691H04L 1/0656H04B 7/0669
80
PatentIndex Score
12
Cited by
17
References
14
Claims

Abstract

In a method for feeding back combination information of transmitted signals in a multiple-input multiple-output (MIMO) system using a multiple space-time block coding technique, mean square error values are computed in relation to the combination information pieces of the transmitted signals. An index of a combination having a minimum mean square error value from among the mean square error values is fed back.

Claims

exact text as granted — not AI-modified
1. A method for feeding back antenna shuffling information of transmitted signals in a multiple-input multiple-output (MIMO) system, comprising the steps of:
 receiving, through two reception antennas, signals transmitted from four transmit antennas; 
 computing mean square error values of the received signals in relation to antenna shuffling information indices of the transmitted signals; and 
 feeding back an index of an antenna shuffling having a minimum mean square error value from among the mean square error values, 
 wherein the index of the antenna shuffling is determined using channel matrix S, where 
 
     
       
         
           
             
               S 
               = 
               
                 [ 
                 
                   
                     
                       
                         h 
                         
                           1 
                           , 
                           1 
                         
                       
                     
                     
                       
                         h 
                         
                           1 
                           , 
                           2 
                         
                       
                     
                     
                       
                         h 
                         
                           1 
                           , 
                           3 
                         
                       
                     
                     
                       
                         h 
                         
                           1 
                           , 
                           4 
                         
                       
                     
                   
                   
                     
                       
                         h 
                         
                           1 
                           , 
                           2 
                         
                         * 
                       
                     
                     
                       
                         - 
                         
                           h 
                           
                             1 
                             , 
                             1 
                           
                           * 
                         
                       
                     
                     
                       
                         h 
                         
                           1 
                           , 
                           4 
                         
                         * 
                       
                     
                     
                       
                         - 
                         
                           h 
                           
                             1 
                             , 
                             3 
                           
                           * 
                         
                       
                     
                   
                   
                     
                       
                         h 
                         
                           2 
                           , 
                           1 
                         
                       
                     
                     
                       
                         h 
                         
                           2 
                           , 
                           2 
                         
                       
                     
                     
                       
                         h 
                         
                           2 
                           , 
                           3 
                         
                       
                     
                     
                       
                         h 
                         
                           2 
                           , 
                           4 
                         
                       
                     
                   
                   
                     
                       
                         h 
                         
                           2 
                           , 
                           2 
                         
                         * 
                       
                     
                     
                       
                         - 
                         
                           h 
                           
                             2 
                             , 
                             1 
                           
                           * 
                         
                       
                     
                     
                       
                         h 
                         
                           2 
                           , 
                           4 
                         
                         * 
                       
                     
                     
                       
                         - 
                         
                           h 
                           
                             2 
                             , 
                             3 
                           
                           * 
                         
                       
                     
                   
                 
                 ] 
               
             
             , 
             
                 
             
             ⁢ 
             and 
           
         
       
       h i,j  is a channel gain value between a j-th Tx antenna and an i-th Rx antenna. 
     
   
   
     2. The method of  claim 1 , wherein the mean square error values are computed in relation to a predetermined number of antenna shuffling information indices from among the antenna shuffling information indices. 
   
   
     3. The method of  claim 1 , wherein the number of antenna shuffling information indices are determined based on a number of transmit antennas. 
   
   
     4. The method of  claim 1 , wherein the minimum mean square error value associated with the antenna shuffling information indices of the transmitted signals is determined by: 
     
       
         
           
             
               
                 λ 
                 
                   q 
                   , 
                   l 
                 
               
               ⁢ 
               
                 = 
                 ZF 
               
               ⁢ 
               
                 
                   min 
                   ⁡ 
                   
                     [ 
                     
                       diag 
                       ⁢ 
                       
                         { 
                         
                           
                             ( 
                             
                               
                                 S 
                                 
                                   q 
                                   , 
                                   
                                     
                                       k 
                                       _ 
                                     
                                     l 
                                   
                                 
                                 H 
                               
                               ⁢ 
                               
                                 S 
                                 
                                   q 
                                   , 
                                   
                                     
                                       k 
                                       _ 
                                     
                                     l 
                                   
                                 
                               
                             
                             ) 
                           
                           
                             - 
                             1 
                           
                         
                         } 
                       
                     
                     ] 
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   = 
                   MMSE 
                 
                 ⁢ 
                 
                   min 
                   ⁡ 
                   
                     [ 
                     
                       diag 
                       ⁢ 
                       
                         { 
                         
                           
                             ( 
                             
                               
                                 
                                   S 
                                   
                                     q 
                                     , 
                                     
                                       
                                         k 
                                         _ 
                                       
                                       l 
                                     
                                   
                                   H 
                                 
                                 ⁢ 
                                 
                                   S 
                                   
                                     q 
                                     , 
                                     
                                       
                                         k 
                                         _ 
                                       
                                       l 
                                     
                                   
                                 
                               
                               + 
                               
                                 
                                   σ 
                                   2 
                                 
                                 ⁢ 
                                 I 
                               
                             
                             ) 
                           
                           
                             - 
                             1 
                           
                         
                         } 
                       
                     
                     ] 
                   
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               q 
               ∈ 
               
                 { 
                 
                   1 
                   , 
                   2 
                   , 
                   … 
                   ⁢ 
                   
                       
                   
                   , 
                   Q 
                 
                 } 
               
             
             , 
             
               l 
               ∈ 
               
                 { 
                 
                   0 
                   , 
                   1 
                   , 
                   … 
                   ⁢ 
                   
                       
                   
                   , 
                   
                     L 
                     - 
                     1 
                   
                 
                 } 
               
             
           
         
       
     
     where diag denotes a diagonal matrix, S denotes the channel matrix, L=T/B, L denotes the number of layers, T denotes the number of transmit antennas, B denotes an STBC block size, Q denotes the number of combinations of the transmitted signals, H denotes a Hermitian transpose, ZF denotes zero forcing, and MMSE denotes a minimum mean square error. 
   
   
     5. The method of  claim 1 , wherein the index of the antenna shuffling having the minimum mean square error value from among the computed mean square error values is determined by: 
     
       
         
           
             
               select 
               ⁢ 
               
                   
               
               ⁢ 
               antenna 
               ⁢ 
               
                   
               
               ⁢ 
               shuffling 
               ⁢ 
               
                   
               
               ⁢ 
               index 
               ⁢ 
               
                   
               
               ⁢ 
               q 
               ⁢ 
               
                   
               
               ⁢ 
               
                 s 
                 . 
                 t 
                 . 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     min 
                     q 
                   
                   ⁢ 
                   
                     ( 
                     
                       min 
                       ⁡ 
                       
                         [ 
                         
                           diag 
                           ⁢ 
                           
                             { 
                             
                               
                                 ( 
                                 
                                   
                                     S 
                                     
                                       q 
                                       , 
                                       
                                         
                                           k 
                                           _ 
                                         
                                         0 
                                       
                                     
                                     H 
                                   
                                   ⁢ 
                                   
                                     S 
                                     
                                       q 
                                       , 
                                       
                                         
                                           k 
                                           _ 
                                         
                                         0 
                                       
                                     
                                   
                                 
                                 ) 
                               
                               
                                 - 
                                 1 
                               
                             
                             } 
                           
                         
                         ] 
                       
                     
                     ) 
                   
                 
               
             
             , 
             
               
                 ( 
                 ZF 
                 ) 
               
               ⁢ 
               
                 ∀ 
                 q 
               
             
           
         
       
       
         
           
             
               
                 min 
                 q 
               
               ⁢ 
               
                 ( 
                 
                   min 
                   ⁡ 
                   
                     [ 
                     
                       diag 
                       ⁢ 
                       
                         { 
                         
                           
                             ( 
                             
                               
                                 
                                   S 
                                   
                                     q 
                                     , 
                                     
                                       
                                         k 
                                         _ 
                                       
                                       0 
                                     
                                   
                                   H 
                                 
                                 ⁢ 
                                 
                                   S 
                                   
                                     q 
                                     , 
                                     
                                       
                                         k 
                                         _ 
                                       
                                       0 
                                     
                                   
                                 
                               
                               + 
                               
                                 
                                   σ 
                                   2 
                                 
                                 ⁢ 
                                 I 
                               
                             
                             ) 
                           
                           
                             - 
                             1 
                           
                         
                         } 
                       
                     
                     ] 
                   
                 
                 ) 
               
             
             , 
             
               
                 ( 
                 MMSE 
                 ) 
               
               ⁢ 
               
                 ∀ 
                 q 
               
             
           
         
       
     
     where diag denotes a diagonal matrix, S denotes the channel matrix, ZF denotes zero forcing, and MMSE denotes a minimum mean square error. 
   
   
     6. The method of  claim 1 , wherein the index of the antenna shuffling having the minimum mean square error value from among the computed mean square error values is determined by: 
     
       
         
           
             
               select 
               ⁢ 
               
                   
               
               ⁢ 
               antenna 
               ⁢ 
               
                   
               
               ⁢ 
               shuffling 
               ⁢ 
               
                   
               
               ⁢ 
               index 
               ⁢ 
               
                   
               
               ⁢ 
               q 
               ⁢ 
               
                   
               
               ⁢ 
               
                 s 
                 . 
                 t 
                 . 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     min 
                     q 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         max 
                         
                           λ 
                           l 
                         
                       
                       ⁢ 
                       
                         [ 
                         
                           min 
                           ⁡ 
                           
                             [ 
                             
                               diag 
                               ⁢ 
                               
                                 { 
                                 
                                   
                                     ( 
                                     
                                       
                                         S 
                                         
                                           q 
                                           , 
                                           
                                             
                                               k 
                                               _ 
                                             
                                             l 
                                           
                                         
                                         H 
                                       
                                       ⁢ 
                                       
                                         S 
                                         
                                           q 
                                           , 
                                           
                                             
                                               k 
                                               _ 
                                             
                                             l 
                                           
                                         
                                       
                                     
                                     ) 
                                   
                                   
                                     - 
                                     1 
                                   
                                 
                                 } 
                               
                             
                             ] 
                           
                         
                         ] 
                       
                     
                     ) 
                   
                 
               
             
             , 
             
               
                 ( 
                 ZF 
                 ) 
               
               ⁢ 
               
                 ∀ 
                 q 
               
             
             , 
             
               ∀ 
               l 
             
           
         
       
       
         
           
             
               
                 min 
                 q 
               
               ⁢ 
               
                 ( 
                 
                   
                     max 
                     
                       λ 
                       l 
                     
                   
                   ⁢ 
                   
                     [ 
                     
                       min 
                       ⁡ 
                       
                         [ 
                         
                           diag 
                           ⁢ 
                           
                             { 
                             
                               
                                 ( 
                                 
                                   
                                     
                                       S 
                                       
                                         q 
                                         , 
                                         
                                           
                                             k 
                                             _ 
                                           
                                           l 
                                         
                                       
                                       H 
                                     
                                     ⁢ 
                                     
                                       S 
                                       
                                         q 
                                         , 
                                         
                                           
                                             k 
                                             _ 
                                           
                                           l 
                                         
                                       
                                     
                                   
                                   + 
                                   
                                     
                                       σ 
                                       2 
                                     
                                     ⁢ 
                                     I 
                                   
                                 
                                 ) 
                               
                               
                                 - 
                                 1 
                               
                             
                             } 
                           
                         
                         ] 
                       
                     
                     ] 
                   
                 
                 ) 
               
             
             , 
             
               
                 ( 
                 MMSE 
                 ) 
               
               ⁢ 
               
                 ∀ 
                 q 
               
             
             , 
             
               ∀ 
               l 
             
           
         
       
     
     where diag denotes a diagonal matrix, S denotes the channel matrix, ZF denotes zero forcing, and MMSE denotes a minimum mean square error. 
   
   
     7. The method of  claim 6 , wherein q denotes a value stored in advance in transmitting and receiving terminals, and denotes an index value of antenna shuffling information of the transmitted signals. 
   
   
     8. The method of  claim 1 , wherein an index of combination information of the transmitted signals is determined by: 
     
       
         
           
             select 
             ⁢ 
             
                 
             
             ⁢ 
             antenna 
             ⁢ 
             
                 
             
             ⁢ 
             shuffling 
             ⁢ 
             
                 
             
             ⁢ 
             index 
             ⁢ 
             
                 
             
             ⁢ 
             q 
             ⁢ 
             
                 
             
             ⁢ 
             
               s 
               . 
               t 
               . 
               
                 
 
               
               ⁢ 
               
                 
                   min 
                   q 
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       abs 
                       [ 
                       
                         det 
                         ⁢ 
                         
                           { 
                           
                             
                               ( 
                               
                                 H 
                                 
                                   q 
                                   , 
                                   1 
                                 
                               
                               ) 
                             
                             + 
                             
                               det 
                               ⁢ 
                               
                                 { 
                                 
                                   ( 
                                   
                                     H 
                                     
                                       q 
                                       , 
                                       2 
                                     
                                   
                                   ) 
                                 
                                 } 
                               
                             
                           
                           ] 
                         
                       
                       ) 
                     
                     , 
                     
                       
                         ( 
                         ZF 
                         ) 
                       
                       ⁢ 
                       
                         ∀ 
                         q 
                       
                     
                   
                 
               
             
           
         
       
     
     where abs denotes an absolute value, det denotes determinant, and ZF denotes zero forcing. 
   
   
     9. An apparatus for transmitting signals in a multiple-input multiple-output (MIMO) system, comprising:
 a shuffling unit for receiving an antenna shuffling index of transmitted signals from a receiving terminal and combining signals to be transmitted according to the antenna shuffling index and assigning the combined signals to antennas; and 
 a MIMO detector for computing mean square error values in relation to antenna shuffling information indices of the transmitted signals, and feeding back an index of an antenna shuffling having a minimum mean square error value from among the mean square error values 
 wherein the index of the antenna shuffling is determined using channel matrix S, where 
 
     
       
         
           
             
               S 
               = 
               
                 [ 
                 
                   
                     
                       
                         h 
                         
                           1 
                           , 
                           1 
                         
                       
                     
                     
                       
                         h 
                         
                           1 
                           , 
                           2 
                         
                       
                     
                     
                       
                         h 
                         
                           1 
                           , 
                           3 
                         
                       
                     
                     
                       
                         h 
                         
                           1 
                           , 
                           4 
                         
                       
                     
                   
                   
                     
                       
                         h 
                         
                           1 
                           , 
                           2 
                         
                         * 
                       
                     
                     
                       
                         - 
                         
                           h 
                           
                             1 
                             , 
                             1 
                           
                           * 
                         
                       
                     
                     
                       
                         h 
                         
                           1 
                           , 
                           4 
                         
                         * 
                       
                     
                     
                       
                         - 
                         
                           h 
                           
                             1 
                             , 
                             3 
                           
                           * 
                         
                       
                     
                   
                   
                     
                       
                         h 
                         
                           2 
                           , 
                           1 
                         
                       
                     
                     
                       
                         h 
                         
                           2 
                           , 
                           2 
                         
                       
                     
                     
                       
                         h 
                         
                           2 
                           , 
                           3 
                         
                       
                     
                     
                       
                         h 
                         
                           2 
                           , 
                           4 
                         
                       
                     
                   
                   
                     
                       
                         h 
                         
                           2 
                           , 
                           2 
                         
                         * 
                       
                     
                     
                       
                         - 
                         
                           h 
                           
                             2 
                             , 
                             1 
                           
                           * 
                         
                       
                     
                     
                       
                         h 
                         
                           2 
                           , 
                           4 
                         
                         * 
                       
                     
                     
                       
                         - 
                         
                           h 
                           
                             2 
                             , 
                             3 
                           
                           * 
                         
                       
                     
                   
                 
                 ] 
               
             
             , 
             
                 
             
             ⁢ 
             and 
           
         
       
       h i,j  is a channel gain value between a j-th Tx antenna and an i-th Rx antenna. 
     
   
   
     10. The apparatus of  claim 9 , further comprising a memory for storing combination information of the transmitted signals corresponding to the antenna shuffling index in advance in a transmitting terminal. 
   
   
     11. The apparatus of  claim 9 , wherein the minimum mean square error value associated with the antenna shuffling information indices of the transmitted signals is determined by: 
     
       
         
           
             
               
                 λ 
                 
                   q 
                   , 
                   l 
                 
               
               ⁢ 
               
                 = 
                 ZF 
               
               ⁢ 
               
                 
                   min 
                   ⁡ 
                   
                     [ 
                     
                       diag 
                       ⁢ 
                       
                         { 
                         
                           
                             ( 
                             
                               
                                 S 
                                 
                                   q 
                                   , 
                                   
                                     
                                       k 
                                       _ 
                                     
                                     l 
                                   
                                 
                                 H 
                               
                               ⁢ 
                               
                                 S 
                                 
                                   q 
                                   , 
                                   
                                     
                                       k 
                                       _ 
                                     
                                     l 
                                   
                                 
                               
                             
                             ) 
                           
                           
                             - 
                             1 
                           
                         
                         } 
                       
                     
                     ] 
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   = 
                   MMSE 
                 
                 ⁢ 
                 
                   min 
                   ⁡ 
                   
                     [ 
                     
                       diag 
                       ⁢ 
                       
                         { 
                         
                           
                             ( 
                             
                               
                                 
                                   S 
                                   
                                     q 
                                     , 
                                     
                                       
                                         k 
                                         _ 
                                       
                                       l 
                                     
                                   
                                   H 
                                 
                                 ⁢ 
                                 
                                   S 
                                   
                                     q 
                                     , 
                                     
                                       
                                         k 
                                         _ 
                                       
                                       l 
                                     
                                   
                                 
                               
                               + 
                               
                                 
                                   σ 
                                   2 
                                 
                                 ⁢ 
                                 I 
                               
                             
                             ) 
                           
                           
                             - 
                             1 
                           
                         
                         } 
                       
                     
                     ] 
                   
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               q 
               ∈ 
               
                 { 
                 
                   1 
                   , 
                   2 
                   , 
                   … 
                   ⁢ 
                   
                       
                   
                   , 
                   Q 
                 
                 } 
               
             
             , 
             
               l 
               ∈ 
               
                 { 
                 
                   0 
                   , 
                   1 
                   , 
                   … 
                   ⁢ 
                   
                       
                   
                   , 
                   
                     L 
                     - 
                     1 
                   
                 
                 } 
               
             
           
         
       
       where diag denotes a diagonal matrix, S denotes the channel matrix, L=T/B, L denotes the number of layers, T denotes the number of transmit antennas, B denotes an STBC block size, Q denotes the number of combinations of the transmitted signals, H denotes a Hermitian transpose, ZF denotes zero forcing, and MMSE denotes a minimum mean square error. 
     
   
   
     12. The apparatus of  claim 9 , wherein the index of the antenna shuffling having the minimum mean square error value from among the computed mean square error values is determined by: 
     
       
         
           
             
               select 
               ⁢ 
               
                   
               
               ⁢ 
               antenna 
               ⁢ 
               
                   
               
               ⁢ 
               shuffling 
               ⁢ 
               
                   
               
               ⁢ 
               index 
               ⁢ 
               
                   
               
               ⁢ 
               q 
               ⁢ 
               
                   
               
               ⁢ 
               
                 s 
                 . 
                 t 
                 . 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     min 
                     q 
                   
                   ⁢ 
                   
                     ( 
                     
                       min 
                       ⁡ 
                       
                         [ 
                         
                           diag 
                           ⁢ 
                           
                             { 
                             
                               
                                 ( 
                                 
                                   
                                     S 
                                     
                                       q 
                                       , 
                                       
                                         
                                           k 
                                           _ 
                                         
                                         0 
                                       
                                     
                                     H 
                                   
                                   ⁢ 
                                   
                                     S 
                                     
                                       q 
                                       , 
                                       
                                         
                                           k 
                                           _ 
                                         
                                         0 
                                       
                                     
                                   
                                 
                                 ) 
                               
                               
                                 - 
                                 1 
                               
                             
                             } 
                           
                         
                         ] 
                       
                     
                     ) 
                   
                 
               
             
             , 
             
               
                 ( 
                 ZF 
                 ) 
               
               ⁢ 
               
                 ∀ 
                 q 
               
             
           
         
       
       
         
           
             
               
                 min 
                 q 
               
               ⁢ 
               
                 ( 
                 
                   min 
                   ⁡ 
                   
                     [ 
                     
                       diag 
                       ⁢ 
                       
                         { 
                         
                           
                             ( 
                             
                               
                                 
                                   S 
                                   
                                     q 
                                     , 
                                     
                                       
                                         k 
                                         _ 
                                       
                                       0 
                                     
                                   
                                   H 
                                 
                                 ⁢ 
                                 
                                   S 
                                   
                                     q 
                                     , 
                                     
                                       
                                         k 
                                         _ 
                                       
                                       0 
                                     
                                   
                                 
                               
                               + 
                               
                                 
                                   σ 
                                   2 
                                 
                                 ⁢ 
                                 I 
                               
                             
                             ) 
                           
                           
                             - 
                             1 
                           
                         
                         } 
                       
                     
                     ] 
                   
                 
                 ) 
               
             
             , 
             
               
                 ( 
                 MMSE 
                 ) 
               
               ⁢ 
               
                 ∀ 
                 q 
               
             
           
         
       
       where diag denotes a diagonal matrix, S denotes the channel matrix, ZF denotes zero forcing, MMSE denotes a minimum mean square error, and q denotes the number of combinations of the transmitted signals. 
     
   
   
     13. The apparatus of  claim 9 , wherein the index of the antenna shuffling having the minimum mean square error value from among the computed mean square error values is determined by: 
     
       
         
           
             
               select 
               ⁢ 
               
                   
               
               ⁢ 
               antenna 
               ⁢ 
               
                   
               
               ⁢ 
               shuffling 
               ⁢ 
               
                   
               
               ⁢ 
               index 
               ⁢ 
               
                   
               
               ⁢ 
               q 
               ⁢ 
               
                   
               
               ⁢ 
               
                 s 
                 . 
                 t 
                 . 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     min 
                     q 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         max 
                         
                           λ 
                           l 
                         
                       
                       ⁢ 
                       
                         [ 
                         
                           min 
                           ⁡ 
                           
                             [ 
                             
                               diag 
                               ⁢ 
                               
                                 { 
                                 
                                   
                                     ( 
                                     
                                       
                                         S 
                                         
                                           q 
                                           , 
                                           
                                             
                                               k 
                                               _ 
                                             
                                             l 
                                           
                                         
                                         H 
                                       
                                       ⁢ 
                                       
                                         S 
                                         
                                           q 
                                           , 
                                           
                                             
                                               k 
                                               _ 
                                             
                                             l 
                                           
                                         
                                       
                                     
                                     ) 
                                   
                                   
                                     - 
                                     1 
                                   
                                 
                                 } 
                               
                             
                             ] 
                           
                         
                         ] 
                       
                     
                     ) 
                   
                 
               
             
             , 
             
               
                 ( 
                 ZF 
                 ) 
               
               ⁢ 
               
                 ∀ 
                 q 
               
             
             , 
             
               ∀ 
               l 
             
           
         
       
       
         
           
             
               
                 min 
                 q 
               
               ⁢ 
               
                 ( 
                 
                   
                     max 
                     
                       λ 
                       l 
                     
                   
                   ⁢ 
                   
                     [ 
                     
                       min 
                       ⁡ 
                       
                         [ 
                         
                           diag 
                           ⁢ 
                           
                             { 
                             
                               
                                 ( 
                                 
                                   
                                     
                                       S 
                                       
                                         q 
                                         , 
                                         
                                           
                                             k 
                                             _ 
                                           
                                           l 
                                         
                                       
                                       H 
                                     
                                     ⁢ 
                                     
                                       S 
                                       
                                         q 
                                         , 
                                         
                                           
                                             k 
                                             _ 
                                           
                                           l 
                                         
                                       
                                     
                                   
                                   + 
                                   
                                     
                                       σ 
                                       2 
                                     
                                     ⁢ 
                                     I 
                                   
                                 
                                 ) 
                               
                               
                                 - 
                                 1 
                               
                             
                             } 
                           
                         
                         ] 
                       
                     
                     ] 
                   
                 
                 ) 
               
             
             , 
             
               
                 ( 
                 MMSE 
                 ) 
               
               ⁢ 
               
                 ∀ 
                 q 
               
             
             , 
             
               ∀ 
               l 
             
           
         
       
       where diag denotes a diagonal matrix, S denotes the channel matrix, ZF denotes zero forcing, MMSE denotes a minimum mean square error, q denotes the number of combinations of the transmitted signals, and l denotes the number of layers determined by the number of transmit antennas and the number of the receive antennas. 
     
   
   
     14. The apparatus of  claim 9 , wherein an index of antenna shuffling information of the transmitted signals is determined by: 
     
       
         
           
             
               select 
               ⁢ 
               
                   
               
               ⁢ 
               antenna 
               ⁢ 
               
                   
               
               ⁢ 
               shuffling 
               ⁢ 
               
                   
               
               ⁢ 
               index 
               ⁢ 
               
                   
               
               ⁢ 
               q 
               ⁢ 
               
                   
               
               ⁢ 
               
                 s 
                 . 
                 t 
                 . 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     min 
                     q 
                   
                   ⁢ 
                   
                     { 
                     
                       abs 
                       ⁡ 
                       
                         [ 
                         
                           
                             det 
                             ⁡ 
                             
                               ( 
                               
                                 H 
                                 
                                   q 
                                   , 
                                   1 
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             det 
                             ⁡ 
                             
                               ( 
                               
                                 H 
                                 
                                   q 
                                   , 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                     
                     } 
                   
                 
               
             
             , 
             
               
                 ( 
                 ZF 
                 ) 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 ∀ 
                 q 
               
             
           
         
       
       where abs denotes an absolute value, det denotes determinant, ZF denotes zero forcing, and q denotes the number of combinations of the transmitted signals.

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